2g ANALYTICAL MECHANICS posts What are the stresses in the different parts of the- trusses when there is a load of 150 pounds per square foot of floor spu.v. |2| t/.'f LA ?^| ! , ..-• f|<.-----------1C .........>)<..........i« . 4, FIG. (a). Fiu- 00- 7. Find the force in one of the members of the truss of figure (b), 8. A weight rests upon a smooth inclined plane, supported by two equal strings the upper ends of which are fastened to two points of the plane in the same horizontal line. Find the tensile force in the strings ami the reaction of the plane. 9. In the preceding problem suppose the piano to bo rough. 10. A particle is suspended by a string which pusses through a smooth ring fastened to the highest point of a circular wire in a vertical plane. The other end of the string is attached to a smooth bowl which Ls movable on the wire. Find the position of equilibrium supposing the bead and the suspended body to have equal weights. 11. A particle is in equilibrium on a rough inclined plane under the action of a force which acts along the plane. If the least mngnit ude of t he force when the inclination of the plane is a equals the greatest magnitude when it is aa, show that <£ = ®l~^: where <£ is the angle of frielion. 2> 12. Two weights W\ and TF2 rest upon a rough inclined plane, connected by a string which passes through a smooth pulley in the plane. Find the greatest inclination the plane can be given without disturbing the equilibrium. 13. Two equal weights, which are connected by a string, rest upon a, rough inclined plane. If the direction of the string is along the .st.eepe.st, slope of the plane and if the coefficients of friction arc; MI and MS, find 11m greatest inclination the plane can be given without disturbing the rqui-librium. 14. In the preceding problem find the tensile force in the string. 15. One end of a uniform rod rests upon a rough peg, while the other end is connected, by means of a string, to a point in the horizontal plant* which contains the peg. When the rod is just on the point of motion it